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Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.

Push-pull substituted fluorenes are considered for use as dynamic solvation probes in polynucleotides. Their fluorescence band is predicted (by simulations) to show weak spectral oscillations on the subpicosecond time scale depending on the nucleotide sequence. The oscillations reflect the local far-infrared spectrum of the environment around the probe molecule. A connection is provided by the continuum theory of polar solvation which, however, neglects molecular aspects. We examine the latter using acetonitrile solution as a test case. A collective librational solvent mode at 100 cm(-1) is observed with 2-amino-7-nitrofluorene, 2-dimethylamino-7-nitrofluorene, 2-hydroxy-7-nitrofluorene, and its 2'-deoxyriboside. Different strengths of the oscillation indicate that rotational friction of nearby acetonitrile molecules depends on the solute structure or that H bonding is involved in launching the librational coherence. Polar solvation in methanol is used for comparison. With hydroxynitrofluorenes, the observation window is limited by intersystem crossing for which rates are reported. A prominent excited-state absorption band of nitrofluorenes at 430 nm can be used to monitor polar solvation. Structural and electronic relaxation pathways are discussed with the help of quantum chemical calculations.

The dynamics of biological processes depend on the structure and flexibility of the interacting molecules. In particular, the conformational diversity of DNA allows for large deformations upon binding. Drug-DNA interactions are of high pharmaceutical interest since the mode of action of anticancer, antiviral, antibacterial and other drugs is directly associated with their binding to DNA. A reliable prediction of drug-DNA binding at the atomic level by molecular docking methods provides the basis for the design of new drug compounds. Here, we propose a novel Monte Carlo (MC) algorithm for drug-DNA docking that accounts for the molecular flexibility of both constituents and samples the docking geometry without any prior binding-site selection. The binding of the antimalarial drug methylene blue at the DNA minor groove with a preference of binding to AT-rich over GC-rich base sequences is obtained in MC simulations in accordance with experimental data. In addition, the transition between two drug-DNA-binding modes, intercalation and minor-groove binding, has been achieved in dependence on the DNA base sequence. The reliable ab initio prediction of drug-DNA binding achieved by our new MC docking algorithm is an important step towards a realistic description of the structure and dynamics of molecular recognition in biological systems.

Photoactive methylene blue is one of the most efficient singlet oxygen generating dyes. It binds to DNA and induces photosensitized reactions which can be used for sequence-specific cleavage of the DNA backbone. Photophysical data obtained for methylene blue in complexes with DNA indicate different binding modes of the dye depending on base sequences. In this study, the binding of methylene blue to a double-stranded decamer with an alternating GC sequence has been investigated by structural modeling and force field based energy calculations. Solvation and desolvation effects have been treated using an electrostatic continuum model. For each of the three possible binding modes (intercalation and minor and major groove binding), a search of the configurational space resulted in six model structures which were selected by the criterion of lowest total energies. The differences of estimated energies are only a few kilocalories per mole, but suggest a preference for symmetric intercalation at the 5‘-CpG-3‘ or ...

The analysis and prediction of non-canonical structural motifs in RNA is of great importance for an understanding of the function and design of RNA structures. A hierarchical method has been employed to generate a large variety of sterically possible conformations for a single-base adenine bulge structure in A -form DNA and RNA. A systematic conformational search was performed on the isolated bulge motif and neighboring nucleotides under the constraint to fit into a continuous helical structure. These substructures were recombined with double-stranded DNA or RNA. Energy minimization resulted in more than 300 distinct bulge conformations. Energetic evaluation using a solvation model based on the finite-difference Poisson-Boltzmann method identified three basic classes of low-energy structures. The three classes correspond to conformations with the bulge base stacked between flanking nucleotides (I), location of the bulge base in the minor groove (II) and conformations with a continuous stacking of the flanking helices and a looped out bulge base (III). For the looped out class, two subtypes (IIIa and IIIb) with different backbone geometries at the bulge site could be distinguished. The conformation of lowest calculated energy was a class I structure with backbone torsion angles close to those in standard A -form RNA. Conformations very close to the extra-helical looped out bulge structure determined by X-ray crystallography were also among the low-energy structures. In addition, topologies observed in other experimentally determined bulge structures have been found among low-energy conformers. The implicit solvent model was further tested by comparing an uridine and adenine bulge flanked by guanine:cytosine base-pairs, respectively. In agreement with the experimental observation, a looped out form was found as the energetically most favorable form for the uridine bulge and a stacked conformation in case of the adenine bulge. The inclusion of solvation effects especially electrostatic reaction field contributions turned out to be critically important in order to select realistic low-energy bulge structures from a large number of sterically possible conformations. The results indicate that the approach might be useful to model the three-dimensional structure of non-canonical motifs embedded in double-stranded RNA, in particular, to restrict the number of possible conformations to a manageable number of conformers with energies below a certain threshold.

An approach to approximately account for receptor flexibility in ligand–receptor docking simulations is described and applied to a DNA/Hoechst 33258 analogue complex. Harmonic modes corresponding to eigenvectors with small eigenvalues of the Hessian matrix of the potential energy function were used as independent variables to describe receptor flexibility. For the DNA minor groove ligand case most of the conformational difference between an energy minimized free DNA and ligand-bound structure could be assigned to 5–40 harmonic receptor modes with small eigenvalues. During docking, deformations of the DNA receptor structure in the subset of harmonic modes were limited using a simple penalty function that avoided the summation over all intrareceptor atom pairs. Significant improvement of the sterical fit between ligand and receptor was found upon relaxation of the DNA in the subset of harmonic modes after docking of the ligand at the position found in the known crystal structure. In addition, the harmonic mode relaxation resulted in DNA structures that were more similar to the energy minimized ligand-bound form. Although harmonic mode relaxation also leads to improved sterical fit for other ligand placements, the placement as observed in the crystal structure could still be identified as the site with the most favorable sterical interactions. Because relaxation in the harmonic modes is orders of magnitude faster than conventional energy minimization using all atom coordinates as independent variables, the approach might be useful as a preselection tool to recognize ligand binding sites accessible only upon small conformational changes of the receptor. The harmonic mode relaxed structures can only be considered as approximate structures because deformation of the receptor in the harmonic modes can lead to small perturbations of the stereochemical geometry of the molecule. Energy minimization of preselected ligand–DNA docking candidates in all atom coordinates is required to reduce these deviations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 287–300, 1999

A combination of conformational search, energy minimization, and energetic evaluation using a continuum solvent treatment has been employed to study the stability of various conformations of the DNA fragment d(CGCAGAA)/d(TTCGCG) containing a single adenine bulge. The extra-helical (looped-out) bulge conformation derived from a published x-ray structure and intra-helical (stacked bulge base) model structures partially based on nuclear magnetic resonance (NMR) data were used as start structures for the conformational search. Solvent-dependent contributions to the stability of the conformations were calculated from the solvent exposed molecular surface area and by using the finite difference Poisson-Boltzmann approach. Three classes (I-III) of bulge conformations with calculated low energies can be distinguished. The lowest-energy conformations were found in class I, corresponding to structures with the bulge base stacked between flanking helices, and class II, composed of structures forming a triplet of the bulge base and a flanking base pair. All extra-helical bulge structures, forming class III, were found to be less stable compared with the lowest energy structures of class I and II. The results are consistent with NMR data on an adenine bulge in the same sequence context indicating an intra-helical or triplet bulge conformation in solution. Although the total energies and total electrostatic energies of the low-energy conformations show only relatively modest variations, the energetic contributions to the stability were found to vary significantly among the classes of bulge structures. All intra-helical bulge structures are stabilized by a more favorable Coulomb charge-charge interaction but destabilized by a larger electrostatic reaction field contribution compared with all extra-helical and most triplet bulge structures. Van der Waals packing interactions and nonpolar surface-area-dependent contributions appear to favor triplet class II structures and to a lesser degree also the intra-helical stacked bulge conformations. The large conformational variation found for class III conformers might add a favorable entropic contribution to the stability of the extra-helical bulge form.

The nonamer duplex d(GCAAAAACG).d(CGTTTTTGC) was studied by 1H-NMR at 500 MHz. With the exception of the H5' and H5" sugar protons, all protons were assigned by two-dimensional NMR experiments [NOE spectroscopy (NOESY), double-quantum-filtered J-correlated spectroscopy (DQF-COSY) and total correlation spectroscopy (TOCSY)]. The exchange kinetics of the imino protons of the Watson-Crick base pairing were studied at 15 degrees C by measuring inversion-recovery rates under conditions of extensive ammonia base catalysis. Extrapolation to infinite base concentration gave anomalous long lifetimes for the A-tract in accordance with previous results [Leroy, J.-L., Charettier, E., Kochoyan, M.Guéron, M. (1988) Biochemistry 27, 8894-8898]. On average, 11 NOESY distance constraints/nucleotide were evaluated using the complete relaxation matrix approach. Deoxyribose coupling constants were obtained from simulations of the DQF-COSY cross-peaks, assuming a rapid two-state equilibrium between a C2'-endo and C3'-endo conformer. The sugars were found to be predominantly in the C2'-endo conformation. The NMR-derived distance and torsion constraints were implemented into three different restrained-molecular-dynamics (rMD) protocols, two in vacuo, with different charges on the phosphate group and the third with the solvent explicitly included. All protocols displayed good convergence from different starting structures. The structures derived from the three protocols satisfied experimental restraints equally well and had similar final energies. Although the overall pattern of sequence dependence of helical parameters shows some resemblance in all structures, we find that the absolute amplitudes of the parameters are largely dependent on the rMD protocols, particularly the twist parameters. The minor groove distance P(n + 2)-P(m + 2) varies from 0.7 nm to 1.2 nm in the three protocols. Still the NOESY-derived anomalously short distances AH2(n)-H1'(m + 1) and AH2(n)-H1'(n + 1), n and m denote complementary residues, which are assumed to be indicative of a compressed minor groove, are kept in all calculated structures.

The latest version of JUMNA program for the energy optimisation of nucleic acids and nucleic acid-ligand complexes is described. The force field used, input and output data, various options for symmetry, conformational constraints and energy mapping are discussed as well as recent combinatorial search techniques.

The atomic coordinates from the crystal structure of a hexasaccharide complex accommodating a zigzag polyiodide [ W. Hinrichs, G. Buttner, M. Steifa, Ch. Betzel, V. Zabel, B. Pfannemuller, and W. Saenger (1987) Science Vol. 238, pp. 205–208; W. Hinrichs and W. Saenger (1990) Journal of the American Chemical Society, Vol. 112, pp. 2789–2796 ] served to construct an antiparallel-stranded amylose double helix with a 5 A wide central cavity. Using our methodology for the energetic optimization of polymer structures in the internal/ helical variable space [ H. Sklenar, R. Lavery, and B. Pullman (1986) Journal of Biomolecular Structure Dynamics, Vol. 3, pp. 967–987, 989–1014; 1015–1031], we have calculated a theoretical counterpart of this idealized double helix by constraining the helical twist and rise to their experimental values (−45° and 2.33 A, respectively). Applying the same constraints to the parallel-stranded duplex, this also leads to a low-energy structure with wide central cavity. It is considered as an alternative model to accommodate iodine as observed in the starch–iodine complex. Release of the helical constraints leads to left-handed antiparallel- and parallel-stranded double helices, respectively, with narrow central cavities. Both structures have very similar helix parameters and correspond, in their main characteristics, to the experimentally derived parallel-stranded structure of amylose in starch (6 residues per turn and a pitch height of about 21 A). The intramolecular energy calculated for the optimized antiparallel-stranded amylose double helix is comparable to that of the parallel-stranded structure. This result raises the question why parallel-stranded amylose seems to be favored in nature. © 1993 John Wiley & Sons, Inc.

In the crystal, d(GGGATCCC)2 forms an A-DNA double helix as known from a single crystal X-ray diffraction study. Accordingly, in the Raman spectra of crystals the A-family marker bands at 664, 705, 807 and 1101 cm-1 and the spectral characteristics in the region 1200 to 1500 cm-1 clearly demonstrate the A-form as the dominant conformation. Bands at 691, 850, and 1080 cm-1, however, indicate that a minor fraction of the octamer molecules in the crystal is in an unusual, still not unequivocally identified conformation possibly belonging to the B-family. In solution, the octamer is in B-like conformation as shown by the presence of B-DNA Raman marker bands at 685, 837, 1094 and 1421 cm-1. Molecular modelling techniques lead to three structures with slightly different B-form geometries as the lowest energies models when a sigmoidal dielectric function with the bulk dielectric constant epsilon = 78 and the value q = -0.5e for the effective phosphate charges was used in the calculations. An A-form structure bearing a strong resemblance to the experimentally determined crystal structure becomes the lowest energy model structure when the electrostatic parameters are changed to epsilon = 30 and q = -0.25e, respectively.

DNA bending is an important structural feature for indirect readout in protein-DNA recognition. The binding of papillomavirus E2 transcription factors to their DNA binding sites is associated with DNA bending, providing an attractive model system to study the origins of sequence-specific DNA bending. The consensus E2 target is of the general form ACCGN(4)CGGT with a variable four base pair region. We applied a new all-atom Monte Carlo (MC) algorithm that combines effective sampling with fast conformational equilibration. The resulting MC ensembles resemble the corresponding high-resolution crystal structures very well. Distinct bending is observed for the E2-DNA binding site with a central AATT linker in contrast to an essentially straight DNA with a central ACGT linker. Contributions of specific base pair steps to the overall bending are shown in terms of local structural parameters. The analysis of conformational substates provides new insights into the energetic origins of intrinsic DNA bending.

The results presented in this paper on methylene blue (MB) binding to DNA with AT alternating base sequence complement the data obtained in two former modeling studies of MB binding to GC alternating DNA. In the light of the large amount of experimental data for both systems, this theoretical study is focused on a detailed energetic analysis and comparison in order to understand their different behavior. Since experimental high-resolution structures of the complexes are not available, the analysis is based on energy minimized structural models of the complexes in different binding modes. For both sequences, four different intercalation structures and two models for MB binding in the minor and major groove have been proposed. Solvent electrostatic effects were included in the energetic analysis by using electrostatic continuum theory, and the dependence of MB binding on salt concentration was investigated by solving the non-linear Poisson-Boltzmann equation. We find that the relative stability of the different complexes is similar for the two sequences, in agreement with the interpretation of spectroscopic data. Subtle differences, however, are seen in energy decompositions and can be attributed to the change from symmetric 5'-YpR-3' intercalation to minor groove binding with increasing salt concentration, which is experimentally observed for the AT sequence at lower salt concentration than for the GC sequence. According to our results, this difference is due to the significantly lower non-electrostatic energy for the minor groove complex with AT alternating DNA, whereas the slightly lower binding energy to this sequence is caused by a higher deformation energy of DNA. The energetic data are in agreement with the conclusions derived from different spectroscopic studies and can also be structurally interpreted on the basis of the modeled complexes. The simple static modeling technique and the neglect of entropy terms and of non-electrostatic solute-solvent interactions, which are assumed to be nearly constant for the compared complexes of MB with DNA, seem to be justified by the results.

A common point of reference is needed to describe the three-dimensional arrangements of bases and base-pairs in nucleic acid structures. The different standards used in computer programs created for this purpose give rise to con¯icting interpretations of the same structure.1 For example, parts of a structure that appear ``normal'' according to one computational scheme may be highly unusual according to another and vice versa. It is thus dif®cult to carry out comprehensive comparisons of nucleic acid structures and to pinpoint unique conformational features in individual structures

The harmonic mode analysis method was used to characterize the conformational deformability of regular Watson-Crick paired, mismatch- and bulge-containing RNA. Good agreement between atomic Debye-Waller factors derived from x-ray crystallography of a regular RNA oligonucleotide and calculated atomic fluctuations was obtained. Calculated helical coordinate fluctuations showed a small sequence dependence of up to approximately 30-50%. A negative correlation between motions at a given base pair step and neighboring steps was found for most helical coordinates. Only very few calculated modes contribute significantly to global motions such as bending, twisting, and stretching of the RNA molecules. With respect to a local helical description of the RNA helix our calculations suggest that RNA bending is mostly due to a periodic change in the base pair step descriptors slide and roll. The presence of single guanine:uridine or guanine:adenine mismatches had little influence on the calculated RNA flexibility. In contrast, for tandem guanine:adenine base pairs the harmonic mode approach predicts a significantly reduced conformational flexibility in the case of a sheared arrangement and slightly enhanced flexibility for a face-to-face (imino proton) pairing relative to regular RNA. The presence of a single extra adenine bulge nucleotide stacked between flanking sequences resulted in an increased local atomic mobility around the bulge site (approximately 40%) and a slightly enhanced global bending flexibility. For an adenine bulge nucleotide in a looped-out conformation a strongly enhanced bulge nucleotide mobility but no increased bending flexibility compared to regular RNA was found.

The protocol of conformational analysis applied here to ribonucleotide oligomers combines conformational search in the space of torsion angles and energy minimization using the AMBER4.1 force field with a continuum treatment of electrostatic solute-solvent interactions. RNA fragments with 5′-GGGCGNNAGCCU-3′ sequences commonly fold into hairpins with four-membered loops. The combinatorial search for acceptable conformations using the MC-SYM program was restricted to loop nucleotides and yielded roughly 1500 structures being compatible with a double-stranded stem. After energy minimization by the JUMNA program (without applying any experimental constraints), these structures converged into an ensemble of 74 different conformers including 26 structures which contained the sheared G-A base pair observed in experimental studies of GNRA tetraloops. Energetic analysis shows that inclusion of solvent electrostatic effects is critically important for the selection of conformers that agree with experimentally determined structures. The continuum model accounts for solvent polarization by means of the electrostatic reaction field. In the case of GNRA loop sequences, the contributions of the reaction field shift relative stabilities towards conformations showing most of the structural features derived from NMR studies. The agreement of computed conformations with the experimental structures of GAAA, GCAA, and GAGA tetraloops suggests that the continuum treatment of the solvent represents a definitive improvement over methods using simple damping models in electrostatic energy calculations. Application of the procedure described here to the evaluation of the relative stabilities of conformers resulting from searching the conformational space of RNA structural motifs provides some progress in (non-homology based) RNA 3D-structure prediction.

Two new databases have been developed to provide the comprehensive research on mechanisms controlling eukaryotic gene expression on the transcription level: TRRD (Transcription Regulatory Region Database) for accumulation of data about structural and functional organisation of gene regulatory regions, and COMPEL - the database on composite regulatory elements that contains contiguous or overlapping binding sites for different transcription factors. Link between TRRD, COMPEL and TRANSFAC through the common table “GENES” has been established. Computer analysis of the transcription regulatory sequences collected in the databases have been carried out by means of SITEVIDEO system. SITEVIDEO offers the following programs: search for significant oligonucleotides in a 15-letter code; dinucleotide weight consensus; analysis of DNA conformation parameters.

A new procedure for the graphic analysis of molecular dynamics (MD) simulations on proteins is introduced, in which comprehensive visualization of results and pattern recognition is greatly facilitated. The method involves determining the conformational and helicoidal parameters for each structure entering the analysis via the method "Curves," developed for proteins by Sklenar, Etchebest, and Lavery (Proteins: Structure, Function Genet. 6:46-60, 1989) followed by a novel computer graphic display of the results. The graphic display is organized systematically using conformation wheels ("dials") for each torsional parameter and "windows" on the range values assumed by the linear and angular helicoidal parameters, and is present in a form isomorphous with the primary structure per se. The complete time evolution of dynamic structure can then be depicted in a set of four composite figures. Dynamic aspects of secondary and tertiary structure are also provided. The procedure is illustrated with an analysis of a 50 psec in vacuo simulation on the 58 residue protein, bovine pancreatic trypsin inhibitor (BPTI), in the vicinity of the local minimum on the energy surface corresponding to a high resolution crystal structure. The time evolution of 272 conformational and 788 helicoidal parameters for BPTI is analyzed. A number of interesting features can be discerned in the analysis, including the dynamic range of conformational and helicoidal motions, the dynamic extent of 2 degrees structure motifs, and the calculated fluctuations in the helix axis. This approach is expected to be useful for a critical analysis of the effects of various assumptions about force field parameters, truncation of potentials, solvation, and electrostatic effects, and can thus contribute to the development of more reliable simulation protocols for proteins. Extensions of the analysis to present differential changes in conformational and helicoidal parameters is expected to be valuable in MD studies of protein complexes with substrates, inhibitors, and effectors and in determining the nature of structural changes in protein-protein interactions.A new procedure for the graphic analysis of molecular dynamics (MD) simulations on proteins is introduced, in which comprehensive visualization of results and pattern recognition is greatly facilitated. The method involves determining the conformational and helicoidal parameters for each structure entering the analysis via the method "Curves," developed for proteins by Sklenar, Etchebest, and Lavery (Proteins: Structure, Function Genet. 6:46-60, 1989) followed by a novel computer graphic display of the results. The graphic display is organized systematically using conformation wheels ("dials") for each torsional parameter and "windows" on the range values assumed by the linear and angular helicoidal parameters, and is present in a form isomorphous with the primary structure per se. The complete time evolution of dynamic structure can then be depicted in a set of four composite figures. Dynamic aspects of secondary and tertiary structure are also provided. The procedure is illustrated with an analysis of a 50 psec in vacuo simulation on the 58 residue protein, bovine pancreatic trypsin inhibitor (BPTI), in the vicinity of the local minimum on the energy surface corresponding to a high resolution crystal structure. The time evolution of 272 conformational and 788 helicoidal parameters for BPTI is analyzed. A number of interesting features can be discerned in the analysis, including the dynamic range of conformational and helicoidal motions, the dynamic extent of 2 degrees structure motifs, and the calculated fluctuations in the helix axis. This approach is expected to be useful for a critical analysis of the effects of various assumptions about force field parameters, truncation of potentials, solvation, and electrostatic effects, and can thus contribute to the development of more reliable simulation protocols for proteins. Extensions of the analysis to present differential changes in conformational and helicoidal parameters is expected to be valuable in MD studies of protein complexes with substrates, inhibitors, and effectors and in determining the nature of structural changes in protein-protein interactions.

International audience; A new procedure for the analysis of the structure and molecular dynamics of duplex DNA is introduced, in which comprehensive visualization of results and pattern recognition is greatly facilitated. The method involves determining the values of the conformational and helicoidal parameters for each structure entering the analysis using the method "Curves" developed by Lavery and Sklenar, J. Biomol. Str. Dyn. 6, 63 (1988), followed by a novel computer graphic display of the results. The graphic display is organized systematically using conformation wheels, or "dials", for each IUPAC torsional parameter and "windows" on the range of values assumed by the linear and angular helicoidal parameters, and is presented in a form isomorphous with the structure per se. The complete time evolution of the conformational and helicoidal parameters of a DNA double helix can then be depicted in a set of six composite figures. Dynamical aspects of helix bending are also subsumed in this analysis. The procedure is illustrated with an analysis of the structures of canonical A and B forms of DNA and the 300 degrees K native dodecamer duplex d(CGCGAATTCGCG). The "dials and windows" are then used for a comprehensive analysis of 30 psec of molecular dynamics on the dodecamer in the vicinity of a canonical B-DNA energy minimum. This involves presentation of the time evolution of 206 conformational and 230 helicoidal parameters for the dodecamer. A number of interesting structural features can be recognized in the analysis, including crankshaft motions, BI - BII transitions, sugar repuckerings, and a description of spontaneous helix bending at what corresponds to the 1 degrees and 2 degrees "hinge points" indicated in the crystal structure. Our approach is expected to be directly useful for critical analysis of the effects of various assumptions about force field parameters, hydration and electrostatic effects and thus contribute to the development of reliable simulation protocols for nucleic acid systems. Extension of the method to present differential changes in conformational and helicoidal parameters is expected to be valuable for the analysis of structural and molecular dynamics studies of the reorganization and adaptation of DNA on complexation with various drugs and regulatory proteins.A new procedure for the analysis of the structure and molecular dynamics of duplex DNA is introduced, in which comprehensive visualization of results and pattern recognition is greatly facilitated. The method involves determining the values of the conformational and helicoidal parameters for each structure entering the analysis using the method "Curves" developed by Lavery and Sklenar, J. Biomol. Str. Dyn. 6, 63 (1988), followed by a novel computer graphic display of the results. The graphic display is organized systematically using conformation wheels, or "dials", for each IUPAC torsional parameter and "windows" on the range of values assumed by the linear and angular helicoidal parameters, and is presented in a form isomorphous with the structure per se. The complete time evolution of the conformational and helicoidal parameters of a DNA double helix can then be depicted in a set of six composite figures. Dynamical aspects of helix bending are also subsumed in this analysis. The procedure is illustrated with an analysis of the structures of canonical A and B forms of DNA and the 300 degrees K native dodecamer duplex d(CGCGAATTCGCG). The "dials and windows" are then used for a comprehensive analysis of 30 psec of molecular dynamics on the dodecamer in the vicinity of a canonical B-DNA energy minimum. This involves presentation of the time evolution of 206 conformational and 230 helicoidal parameters for the dodecamer. A number of interesting structural features can be recognized in the analysis, including crankshaft motions, BI - BII transitions, sugar repuckerings, and a description of spontaneous helix bending at what corresponds to the 1 degrees and 2 degrees "hinge points" indicated in the crystal structure. Our approach is expected to be directly useful for critical analysis of the effects of various assumptions about force field parameters, hydration and electrostatic effects and thus contribute to the development of reliable simulation protocols for nucleic acid systems. Extension of the method to present differential changes in conformational and helicoidal parameters is expected to be valuable for the analysis of structural and molecular dynamics studies of the reorganization and adaptation of DNA on complexation with various drugs and regulatory proteins.

International audience; The algorithm "Curves", that we have recently presented in this journal (J. Biolmol. Str. Dynam. 6, 63-91 (1988], is updated to take into account the conventions developed at the Cambridge meeting on DNA curvature (September 1988) and extended to the calculation of local parameters. In addition, the principles which govern the choices made in establishing the Curves algorithm are compared with the approaches adopted by other authors.The algorithm "Curves", that we have recently presented in this journal (J. Biolmol. Str. Dynam. 6, 63-91 (1988], is updated to take into account the conventions developed at the Cambridge meeting on DNA curvature (September 1988) and extended to the calculation of local parameters. In addition, the principles which govern the choices made in establishing the Curves algorithm are compared with the approaches adopted by other authors.

A numerical method for the calculation of bound states in a one-dimensional potential is suggested, the application of which is very simple and economic. The wavefunctions as well as the potential are approximated by Lagrange interpolation polynomials of the order 2N. The application of the variational principle yields a (2N−1)th order eigenvalue problem of the symmetric matrix H derived from the universal matrices' T and V (l) (l = 0,1,..., N) and (2N + 1) discrete potential values of the actual problem by means of simple matrix algebra. The accuracy of the obtained energies and wavefunctions depends on the parameter N. The proposed method has been applied to different types of potentials. Using polynomials of the order twenty (N=10), generally the results are quite satisfactory for the states of quantum numbers n≦4.

The binding energies of N 2 to Na + and K + are computed, using the SCF supermolecule approach with extended basis sets together with the counterpoise correction computed in two extreme ways, and supplemented by a perturbation calculation of the dispersion energy. Inclusion of the calculated zero-point energy and the additional correction due to the variation of the correlation in N 2 upon complexation leads to an Na + -N 2 binding of −7.9 to −8.1 kcal/mole (compared to a measured enthalpy of −8 ± 0.5) and to a corresponding theoretical value computed for K + -N 2 of −4.6 to −4.8 kcal/mole.

Detailed quantum-chemical calculations by means of semiempirical all-valence electrons methods and a generalized (multivariable) rank correlation analysis are the fundamentals of a novel strategy of search for QSAR within homologous series of compounds. The set of molecular parameters (describing the electronic and conformational properties as well as potential interactions of the drugs) is calculated theoretically. Owing to the rank correlation method, no linear model (like LFER) for the dependence of the biological activity upon the molecular parameters is presumed. The computed correlation coefficients are valued by carefully determined levels of statistical significance. Significant correlations are used to predict unknown activities in terms of ranks relative to the basic sample.

Molecular dynamics (MD) simulations including water and counterions on B-DNA oligomers containing all 136 unique tetranucleotide basepair steps are reported. The objective is to obtain the calculated dynamical structure for at least two copies of each case, use the results to examine issues with regard to convergence and dynamical stability of MD on DNA, and determine the significance of sequence context effects on all unique dinucleotide steps. This information is essential to understand sequence effects on DNA structure and has implications on diverse problems in the structural biology of DNA. Calculations were carried out on the 136 cases embedded in 39 DNA oligomers with repeating tetranucleotide sequences, capped on both ends by GC pairs and each having a total length of 15 nucleotide pairs. All simulations were carried out using a well-defined state-of-the-art MD protocol, the AMBER suite of programs, and the parm94 force field. In a previous article (Beveridge et al. 2004. Biophysical Journal. 87:3799-3813), the research design, details of the simulation protocol, and informatics issues were described. Preliminary results from 15 ns MD trajectories were presented for the d(CpG) step in all 10 unique sequence contexts. The results indicated the sequence context effects to be small for this step, but revealed that MD on DNA at this length of trajectory is subject to surprisingly persistent cooperative transitions of the sugar-phosphate backbone torsion angles alpha and gamma. In this article, we report detailed analysis of the entire trajectory database and occurrence of various conformational substates and its impact on studies of context effects. The analysis reveals a possible direct correspondence between the sequence-dependent dynamical tendencies of DNA structure and the tendency to undergo transitions that "trap" them in nonstandard conformational substates. The difference in mean of the observed basepair step helicoidal parameter distribution with different flanking sequence sometimes differs by as much as one standard deviation, indicating that the extent of sequence effects could be significant. The observations reveal that the impact of a flexible dinucleotide such as CpG could extend beyond the immediate basepair neighbors. The results in general provide new insight into MD on DNA and the sequence-dependent dynamical structural characteristics of DNA.Molecular dynamics (MD) simulations including water and counterions on B-DNA oligomers containing all 136 unique tetranucleotide basepair steps are reported. The objective is to obtain the calculated dynamical structure for at least two copies of each case, use the results to examine issues with regard to convergence and dynamical stability of MD on DNA, and determine the significance of sequence context effects on all unique dinucleotide steps. This information is essential to understand sequence effects on DNA structure and has implications on diverse problems in the structural biology of DNA. Calculations were carried out on the 136 cases embedded in 39 DNA oligomers with repeating tetranucleotide sequences, capped on both ends by GC pairs and each having a total length of 15 nucleotide pairs. All simulations were carried out using a well-defined state-of-the-art MD protocol, the AMBER suite of programs, and the parm94 force field. In a previous article (Beveridge et al. 2004. Biophysical Journal. 87:3799-3813), the research design, details of the simulation protocol, and informatics issues were described. Preliminary results from 15 ns MD trajectories were presented for the d(CpG) step in all 10 unique sequence contexts. The results indicated the sequence context effects to be small for this step, but revealed that MD on DNA at this length of trajectory is subject to surprisingly persistent cooperative transitions of the sugar-phosphate backbone torsion angles alpha and gamma. In this article, we report detailed analysis of the entire trajectory database and occurrence of various conformational substates and its impact on studies of context effects. The analysis reveals a possible direct correspondence between the sequence-dependent dynamical tendencies of DNA structure and the tendency to undergo transitions that "trap" them in nonstandard conformational substates. The difference in mean of the observed basepair step helicoidal parameter distribution with different flanking sequence sometimes differs by as much as one standard deviation, indicating that the extent of sequence effects could be significant. The observations reveal that the impact of a flexible dinucleotide such as CpG could extend beyond the immediate basepair neighbors. The results in general provide new insight into MD on DNA and the sequence-dependent dynamical structural characteristics of DNA.

We describe herein a computationally intensive project aimed at carrying out molecular dynamics (MD) simulations including water and counterions on B-DNA oligomers containing all 136 unique tetranucleotide base sequences. This initiative was undertaken by an international collaborative effort involving nine research groups, the "Ascona B-DNA Consortium" (ABC). Calculations were carried out on the 136 cases imbedded in 39 DNA oligomers with repeating tetranucleotide sequences, capped on both ends by GC pairs and each having a total length of 15 nucleotide pairs. All MD simulations were carried out using a well-defined protocol, the AMBER suite of programs, and the parm94 force field. Phase I of the ABC project involves a total of approximately 0.6 mus of simulation for systems containing approximately 24,000 atoms. The resulting trajectories involve 600,000 coordinate sets and represent approximately 400 gigabytes of data. In this article, the research design, details of the simulation protocol, informatics issues, and the organization of the results into a web-accessible database are described. Preliminary results from 15-ns MD trajectories are presented for the d(CpG) step in its 10 unique sequence contexts, and issues of stability and convergence, the extent of quasiergodic problems, and the possibility of long-lived conformational substates are discussed.We describe herein a computationally intensive project aimed at carrying out molecular dynamics (MD) simulations including water and counterions on B-DNA oligomers containing all 136 unique tetranucleotide base sequences. This initiative was undertaken by an international collaborative effort involving nine research groups, the "Ascona B-DNA Consortium" (ABC). Calculations were carried out on the 136 cases imbedded in 39 DNA oligomers with repeating tetranucleotide sequences, capped on both ends by GC pairs and each having a total length of 15 nucleotide pairs. All MD simulations were carried out using a well-defined protocol, the AMBER suite of programs, and the parm94 force field. Phase I of the ABC project involves a total of approximately 0.6 mus of simulation for systems containing approximately 24,000 atoms. The resulting trajectories involve 600,000 coordinate sets and represent approximately 400 gigabytes of data. In this article, the research design, details of the simulation protocol, informatics issues, and the organization of the results into a web-accessible database are described. Preliminary results from 15-ns MD trajectories are presented for the d(CpG) step in its 10 unique sequence contexts, and issues of stability and convergence, the extent of quasiergodic problems, and the possibility of long-lived conformational substates are discussed.

International audience; Results concerning the flexibility of mononucleotide repeat DNA are presented using a novel methodology, denoted "SIR", to describe continuous changes in the structure of the nucleic acid. This methodology, combined with internal energy calculations and analytical energy gradients allows us to determine optimal conformations of poly(dG).poly(dC) and poly (dA).poly(dT) in both the A and B forms, taking into account the influence of the solvent medium and explicit counterions. Subsequently, several different types of distorsion of these optimal structures are investigated. It is shown that excellent correlation with experimental results concerning coupled changes in structural variables is obtained and several new correlations are also detected.Results concerning the flexibility of mononucleotide repeat DNA are presented using a novel methodology, denoted "SIR", to describe continuous changes in the structure of the nucleic acid. This methodology, combined with internal energy calculations and analytical energy gradients allows us to determine optimal conformations of poly(dG).poly(dC) and poly (dA).poly(dT) in both the A and B forms, taking into account the influence of the solvent medium and explicit counterions. Subsequently, several different types of distorsion of these optimal structures are investigated. It is shown that excellent correlation with experimental results concerning coupled changes in structural variables is obtained and several new correlations are also detected.

We present a general and mathematically rigorous algorithm which allows the helicoidal structure of a protein to be calculated starting from the atomic coordinates of its peptide backbone. This algorithm yields a unique curved axis which quantifies the folding of the backbone and a full set of helicoidal parameters describing the location of each peptide unit. The parameters obtained form a complete and independent set and can therefore be used for analyzing, comparing, or reconstructing protein backbone geometry. This algorithm has been implemented in a computer program named P-Curve. Several examples of its possible applications are discussed.We present a general and mathematically rigorous algorithm which allows the helicoidal structure of a protein to be calculated starting from the atomic coordinates of its peptide backbone. This algorithm yields a unique curved axis which quantifies the folding of the backbone and a full set of helicoidal parameters describing the location of each peptide unit. The parameters obtained form a complete and independent set and can therefore be used for analyzing, comparing, or reconstructing protein backbone geometry. This algorithm has been implemented in a computer program named P-Curve. Several examples of its possible applications are discussed.

International audience; A novel and powerful methodology is developed which allows the alteration of molecular structures subjected to constraints and its application to polynucleotides with mononucleotide repeat symmetry, including the treatment of the flexible sugar rings is described. In contrast to procedures proposed by other authors, the constraints are formulated as differential equations which are linear with respect to the differentials of the geometrical variables. These equations can be solved easily by stepwise numerical integration involving sucessive infinitesimal rotations (SIR). Moreover, these equations define a set of independent curvilinear coordinates which can be used directly as the parameters of the energy functional in an energy minimisation procedure. This methodology allows the scanning of the full configurational space of a complex macromolecule, with direct access to the helicoidal variables in the case of periodic systems. Through this approach many problems involving biomacromolecular conformation, which would otherwise be intractable, may be studied with considerable ease.A novel and powerful methodology is developed which allows the alteration of molecular structures subjected to constraints and its application to polynucleotides with mononucleotide repeat symmetry, including the treatment of the flexible sugar rings is described. In contrast to procedures proposed by other authors, the constraints are formulated as differential equations which are linear with respect to the differentials of the geometrical variables. These equations can be solved easily by stepwise numerical integration involving sucessive infinitesimal rotations (SIR). Moreover, these equations define a set of independent curvilinear coordinates which can be used directly as the parameters of the energy functional in an energy minimisation procedure. This methodology allows the scanning of the full configurational space of a complex macromolecule, with direct access to the helicoidal variables in the case of periodic systems. Through this approach many problems involving biomacromolecular conformation, which would otherwise be intractable, may be studied with considerable ease.

International audience; An algorithm is presented which solves the problem of obtaining a rigorous helicoidal description of an irregular nucleic acid segment. Central to this approach is the definition of a function describing simultaneously the curvature of the nucleic acid segment in question and the corresponding stepwise variation of helicoidal parameters along the segment. Minimisation of this function leads to an optimal distribution of the conformational irregularity of the segment between these two components. Further, it is shown that this approach can be applied equally easily to single or double stranded nucleic acids. The results of this analysis yield both the absolute helicoidal parameters of individual bases/base pairs and the relative helicoidal parameters between successive bases/base pairs as well as the overall locus of the helical axis. The possibilities of this mathematical approach are demonstrated with the help of a computer program termed "Curves" which is applied to the study of a number of different nucleic acid structures.An algorithm is presented which solves the problem of obtaining a rigorous helicoidal description of an irregular nucleic acid segment. Central to this approach is the definition of a function describing simultaneously the curvature of the nucleic acid segment in question and the corresponding stepwise variation of helicoidal parameters along the segment. Minimisation of this function leads to an optimal distribution of the conformational irregularity of the segment between these two components. Further, it is shown that this approach can be applied equally easily to single or double stranded nucleic acids. The results of this analysis yield both the absolute helicoidal parameters of individual bases/base pairs and the relative helicoidal parameters between successive bases/base pairs as well as the overall locus of the helical axis. The possibilities of this mathematical approach are demonstrated with the help of a computer program termed "Curves" which is applied to the study of a number of different nucleic acid structures.

International audience; A theoretical modelling of the interaction of putrescine (H3+N-(CH2)4-(+NH3) with DNA is carried out, introducing two new features which make the simulation of this interaction considerably more realistic. Firstly, the DNA to which putrescine is bound is fully flexible and thus able to respond to the distorting influence of the ligand. Secondly, the effect of changing the ratio of DNA base pairs per bound ligand is explicitly modelled. In this way, we have been able to confirm the experimentally known preference of putrescine binding with AT base pairs in B-DNA, but we also show, through the new features introduced, that the nature of the binding site of the ligand and the resulting impact on DNA conformation is strongly modified by the ligand binding density.A theoretical modelling of the interaction of putrescine (H3+N-(CH2)4-(+NH3) with DNA is carried out, introducing two new features which make the simulation of this interaction considerably more realistic. Firstly, the DNA to which putrescine is bound is fully flexible and thus able to respond to the distorting influence of the ligand. Secondly, the effect of changing the ratio of DNA base pairs per bound ligand is explicitly modelled. In this way, we have been able to confirm the experimentally known preference of putrescine binding with AT base pairs in B-DNA, but we also show, through the new features introduced, that the nature of the binding site of the ligand and the resulting impact on DNA conformation is strongly modified by the ligand binding density.

This article describes a method for solving the geometric closure problem for simplified models of nucleic acid structures by using the constant bond lengths approximation. The resulting chain breakage/closure equations, formulated in the space of variable torsion and bond angles, are easy to solve, and have only two solutions. The analytical simplicity is in contrast with the high complexity of the closure problem in the torsion angle space with at most 16 solutions, which has been dealt with by several authors and was solved analytically by Wu and Deem (J. Chem. Phys. 1999, 111, 6625). The discussion on the choice of variables and associated Jacobians is focussed on the question of how conformational equilibration is affected in Monte Carlo simulations of molecular systems. In addition to the closure of the phosphate backbone, it is necessary to also solve the closure problem for the five-membered flexible furanose sugar ring. Explicit closure equations and the resulting Jacobians are given both for the complete four-variable model of the furanose ring and simulations in the phase-amplitude space of the five-membered ring, which are based on the approximate two-variable model of furanose introduced by Gabb et al. (J. Comput. Chem. 1995, 16, 667). The suggested closure algorithm can be combined with collective variables defined by translations and rotations of the monomeric nucleotide units. In comparison with simple internal coordinate moves, the resulting concerted moves describe local structural changes that have high acceptance rates and enable fast conformational equilibration. Appropriate molecular models are put forward for prospective Monte Carlo simulations of nucleic acids, but can be easily adapted to other biomolecular systems, such as proteins and lipid structures in biological membranes.